## Abstract

The packing chromatic number χ_{ρ}(*G*) of a graph *G* is the smallest integer *k* such that its set of vertices *V*(*G*) can be partitioned into *k* disjoint subsets *V*
_{1}, . . . , *V _{k}*, in such a way that every two distinct vertices in

*V*are at distance greater than

_{i}*i*in

*G*for every

*i*, 1 ≤

*i*≤

*k*. For a given integer

*p*≥ 1, the

*p*-corona of a graph

*G*is the graph obtained from

*G*by adding

*p*degree-one neighbors to every vertex of

*G*. In this paper, we determine the packing chromatic number of

*p*-coronae of paths and cycles for every

*p*≥ 1.

Moreover, by considering digraphs and the (weak) directed distance between vertices, we get a natural extension of the notion of packing coloring to digraphs. We then determine the packing chromatic number of orientations of *p*-coronae of paths and cycles.